$\overline{AC}$ is $8$ units long $\overline{BC}$ is $6$ units long $\overline{AB}$ is $10$ units long What is $\csc(\angle ABC)?$ $A$ $C$ $B$ $8$ $6$ $10$
Solution: $\csc(\angle ABC) = \dfrac{1}{\sin(\angle ABC)}$ How can we find $\sin(\angle ABC)$ SOH CAH TOA in = pposite over ypotenuse Opposite $= \overline{AC} = 8$ Hypotenuse $= \overline{AB} = 10$ $\sin(\angle ABC) = \dfrac{8}{10}$ $\csc(\angle ABC) = \dfrac{1}{\sin(\angle ABC)} = \dfrac{10}{8}$